516 research outputs found
Quantization and Compressive Sensing
Quantization is an essential step in digitizing signals, and, therefore, an
indispensable component of any modern acquisition system. This book chapter
explores the interaction of quantization and compressive sensing and examines
practical quantization strategies for compressive acquisition systems.
Specifically, we first provide a brief overview of quantization and examine
fundamental performance bounds applicable to any quantization approach. Next,
we consider several forms of scalar quantizers, namely uniform, non-uniform,
and 1-bit. We provide performance bounds and fundamental analysis, as well as
practical quantizer designs and reconstruction algorithms that account for
quantization. Furthermore, we provide an overview of Sigma-Delta
() quantization in the compressed sensing context, and also
discuss implementation issues, recovery algorithms and performance bounds. As
we demonstrate, proper accounting for quantization and careful quantizer design
has significant impact in the performance of a compressive acquisition system.Comment: 35 pages, 20 figures, to appear in Springer book "Compressed Sensing
and Its Applications", 201
Scalable Nearest Neighbor Search with Compact Codes
An important characteristic of the recent decade is the dramatic growth in the use and generation of data. From collections of images, documents and videos, to genetic data, and to network traffic statistics, modern technologies and cheap storage have made it possible to accumulate huge datasets. But how can we effectively
use all this data? The growing sizes of the modern datasets make it crucial to develop new algorithms and tools capable of sifting through this data efficiently. A central computational primitive for analyzing large datasets is the Nearest Neighbor Search problem in which the goal is to preprocess a set of objects, so that later, given a query object, one can find the data object closest to the query. In most situations involving high-dimensional objects, the exhaustive search which compares the query with every item in the dataset has a prohibitive cost both for runtime and memory space. This thesis focuses on the design of algorithms and tools for fast and cost efficient nearest neighbor search. The proposed techniques advocate the use of compressed and discrete codes for representing the neighborhood structure of data in a compact way. Transforming high-dimensional items, such as raw images, into similarity-preserving compact codes has both computational and storage advantages as compact codes can be stored efficiently using only a few bits per data item, and more importantly they can be compared extremely fast using bit-wise or look-up table operators. Motivated by this view, the present work explores two main research directions: 1) finding mappings that better preserve the given notion of similarity while keeping the codes as compressed as possible, and 2) building efficient data structures that support non-exhaustive search among the compact codes. Our large-scale experimental results reported on various benchmarks including datasets upto one billion items, show boost in retrieval performance in comparison to the state-of-the-art
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